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Math Help - Prove recurrance relation

  1. #1
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    Prove recurrance relation

    Prove the recurrence relation d/dx Hn(x) = 2nH(n−1(x)) for n = 0, 1, 2, ..

    I think this has something to do with differentiating the generating function, maybe? But i can't see how it would work.

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  2. #2
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    Are those the Hermite polynomials?
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  3. #3
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    yes they are
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  4. #4
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    Ah. In that case, I'd go for the Rodriguez representation. Are you doing the probability version, or the physics version of the Hermites?
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  5. #5
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    Physics. I know the form of rodriguez representation. But i dont understand how that can be used to answer my question?
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  6. #6
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    Why don't you just try differentiating it and see what happens?
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  7. #7
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    I have done so, but i can't get anything that resembles the RHS, im left with:

    (-1)^2 exp(x^2) (2x+1) + exp(-x^2) (d^n+1/dx^n+1 + d^n/dx^n).

    Any idea? thanks
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  8. #8
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    Look at this thread. It works out if you take the derivative correctly, which I'm not sure you did.
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  9. #9
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    ahhh i see how, using the identity on that thread.

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  10. #10
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    You're welcome. Have a good one!
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